This scenario is very complicated, but is easier than it looks. With a few tips and tricks you too can achieve total religious supremacy.

The easiest way to win is to fully commit to being either stealthy or aggressive.

Stealth tips:
-Start in a really populated country or one with busy air/sea ports. Right off the bat, evolve Cult Compounds and build one there.
-Always keep your vampire cult leader moving! Also evolve Empathy/Celebrity and pay attention to the news bar so you convert as many people in a country as possible before you have to move on.
-Keep your severity down for as long as you can, even after you're discovered. Evolve Legal Team right away and PR Agency around the time the cure starts. Best early symptoms are Agrarianism, Sci-Fi Inspiration, and Astrology. Spend your time buying transmissions.
-You should have at least 3 compounds before the Templars show up. Space them out and evolve Tithes and Delegation to make them more useful.
-By the time the Templars spawn you should already own most of the world and the cure should be <10%. Your compounds should give you tons of DNA for buying combat upgrades.
-Don't be surprised if this strategy takes >700 days.

Aggressive tips:
-Start in a rich country. UK, USA, or Japan are ideal.
-Right off the bat evolve Terrorism and start killing. Spend the rest of your starting DNA on Front Organizations, Empathy, and combat/travel traits. Saving up for Biological/Chemical warfare is often better than the cheaper combat upgrades.
-Rush the Templars the moment they spawn. Place compounds as you move around the map, and evolve Delegation. Evolve Looting instead of Panic Rooms so you can heal while on the offensive. When a WHO lab spawns, immediately focus on it and then go back to the Templars.
-You may want to get Power Struggle after converting over 400 million people.
-With WHO and the Templars out of the way, send out your leaders to convert countries one by one. Keep using Terror Attacks. Evolve Syncretism and one or two integration traits, and pump up your infectivity. On higher difficulties you might need Legal Team and Bribery/Blackmail to hold back the cure.
-This is the best strategy for beating Mega Brutal.

General tips:
-To win the scenario you have to evolve either Doomsday or Mass Suicide. These traits are in the middle of the symptom sprawl. The fastest way to reach them is Messianism>Conspiracy Theories>Apocalypticism (high infectivity) or Body Modification>Animal Sacrifice>Human Sacrifice (high severity/lethality).
-When it comes to starting genes, Brawler, Budget Bat, Native Biome, and Extremophile are usually best. Consider choosing Mad Scientist for your last gene because this is a busy scenario and auto-popping bubbles will let you concentrate on other things.
-Once you fully convert a country its government will go into exile, crippling its cure research. If you have Doomsday research will stop completely.
-There's a lot of popups so don't forget the Escape or Enter keys can close them by default.